Encoding range minima and range top-2 queries

Davoodi, Pooya; Navarro, Gonzalo; Raman, Rajeev; Rao, S. Srinivasa

doi:10.1098/rsta.2013.0131

Cited by 20 publications

(52 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since there are 1 2n+1 2n n binary trees on n + 1 nodes, the effective entropy works out to be 2n − O(log n) bits, and Fischer and Heun gave a 2n + o(n)-bit data structure that answers RMQ in O(1) time 1 . Davoodi et al [4,3] gave alternative 2n + o(n)-bit data structures.…”

Section: Range Statistics On 1d-arraysmentioning

confidence: 99%

Encoding Data Structures

Raman

2015

WALCOM: Algorithms and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Range Statistics On 1d-arraysmentioning

confidence: 99%

Encoding Data Structures

Raman

2015

WALCOM: Algorithms and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…, x t . We do not represent Y itself, but rather store a range top-2 encoding of it [11]. This structure requires O(t) = O(n/κ) bits and returns the positions of the first and second maxima in Y [m, M ], x r and x s , in O(1) time.…”

Section: Shallow Cuttings In Succinct Spacementioning

confidence: 99%

Asymptotically Optimal Encodings of Range Data Structures for Selection and Top- k Queries

Grossi

Iacono

Navarro

et al. 2017

ACM Trans. Algorithms

Self Cite

View full text Add to dashboard Cite

Given an array A[1, n] of elements with a total order, we consider the problem of building a data structure that solves two queries: (a) selection queries receive a range [i, j] and an integer k and return the position of the kth largest element in A[i, j]; (b) top-k queries receive [i, j] and k and return the positions of the k largest elements in A [i, j]. These problems can be solved in optimal time, O(1 + lg k/ lg lg n) and O(k), respectively, using linear-space data structures.We provide the first study of the encoding data structures for the above problems, where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A, and their positions, rather their actual values, and thus we do not need to keep A at query time. In those cases, encodings save storage space: we first show that any encoding answering such queries requires n lg k − O(n + k lg k) bits of space; then, we design encodings using O(n lg k) bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.

show abstract

“…The binary tree structure of Davoodi et al [4] essentially applies Lemma 5 twice to the input tree, getting a set of O(…”

Section: Algorithm 1 Computing Nnlv(a I)mentioning

confidence: 99%

Encoding nearest larger values

Hoffmann

Iacono

Nicholson

et al. 2018

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. In nearest larger value (NLV) problems, we are given an array A[1..n] of numbers, and need to preprocess A to answer queries of the following form: given any index i ∈ [1, n], return a "nearest" index j such that A[j] > A [i]. We consider the variant where the values in A are distinct, and we wish to return an index j such that A[j] > A [i] and |j − i| is minimized, the nondirectional NLV (NNLV) problem. We consider NNLV in the encoding model, where the array A is deleted after preprocessing, and note that NNLV encoding problem has an unexpectedly rich structure: the effective entropy (optimal space usage) of the problem depends crucially on details in the definition of the problem. Using a new path-compressed representation of binary trees, that may have other applications, we encode NNLV in 1.9n + o(n) bits, and answer queries in O(1) time.

show abstract

Encoding range minima and range top-2 queries

Cited by 20 publications

References 15 publications

Encoding Data Structures

Encoding Data Structures

Asymptotically Optimal Encodings of Range Data Structures for Selection and Top- k Queries

Encoding nearest larger values

Contact Info

Product

Resources

About